Cloud computing and IT-service provisioning is critical for the growth of enterprises in being able to provision computationally intensive applications. A high-speed networks infrastructure is necessary for the proliferation of cloud computing to meet disparate IT application demands. Light-trails - a generalization of lightpath with ability to provision sub-wavelength demands, meet dynamic bandwidth needs and cater to optical multicasting in a low-cost platform are investigated as a candidate technology for cloud computing. A time-slotted light-trail system is assumed and an algorithm is proposed based on utility concepts. Scheduling connections over light-trails in a timely manner to meet the tasks of an IT-service are considered. Memory resource management as a constraint is further incorporated in the algorithm thereby making the IT application pragmatically reside over the light-trails infrastructure. An exhaustive simulations study showcases the benefits of light-trails for cloud computing - the results obtained are over a wide range of services with serial, parallel and mixed set of constituent tasks.